Monotone linear transformations on matrices are invertible

Anna A. Alieva, Alexander E. Guterman

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


We show that monotone linear transformations on matrices with respect to <̄, <*, * <, < *, <, < σ, <σ1-partial orders are invertible and provide a complete characterization of such transformations.

Original languageEnglish
Pages (from-to)3335-3352
Number of pages18
JournalCommunications in Algebra
Issue number9
StatePublished - 1 Aug 2005
Externally publishedYes

Bibliographical note

Funding Information:
This work is partially supported by RFBR, grants YSF 03-55-1919 and NSH-1910.2003.01.


  • Linear preservers
  • Matrix partial orders
  • Monotone transformations


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